I don't want to leave earth without understanding math.

Carol S. Dweck is one of those people I don’t read. It’s nothing to do with her—as you’ll soon see, I have come around to loving her work—but the fact that I don’t read books that seem actively primed to rewire my brain. It’s a delicate thing, you know?

Recently, I came across this quote of hers on Goodreads:

“In the fixed mindset, everything is about the outcome. If you fail—or if you’re not the best—it’s all been wasted. The growth mindset allows people to value what they’re doing regardless of the outcome . They’re tackling problems, charting new courses, working on important issues. Maybe they haven’t found the cure for cancer, but the search was deeply meaningful.”

The aspects of Carol’s work I’m aware of focus on this idea of a “growth mindset”. It speaks about two types of mental states/mindsets:

1. The fixed mindset. It believes its current outcomes are immovable, or at least can’t be changed significantly enough to matter.
2. The growth mindset. This is the mindset that winners have. They never take Ls. Every failure is valuable feedback. They go again.

I realized, while reading this, that if there’s any truth to this theory, then I am surprised. I initially assumed people had growth mindsets or fixed mindsets, but looking at my own life, I realize people have to be a mix of fixed and growth mindsets.

There are many experiences I’ve found myself deeply involved in simply because I had a growth mindset. In fact, I tend to have a growth mindset when it comes to my own prospects.

Which is why, over the years, it started to get glaringly sus that I fear math.

And it is fear. The idea of a math equation causes a curious and small flutter in my heart. A flight response, in fact. Why?

I realize, in retrospect, that it’s because I missed something crucial to understanding math. I’m not blaming my tutors, because who knows if I was even paying attention in school? (By the way, this is also a hint: you can skate by in life barely paying attention. Not so with math).

What did I miss?

Cards on the table.

The one thing I really never internalized is that math follows reason. It’s perfectly rational. You should be able to follow every single idea and construction from your own intuition.

For some reason, I assumed some aspects of math were unknowable. Like, it was just received knowledge. I never thought to probe into who gifted the knowledge.

Speaking of which, do you know my fear of math started to lessen when I started reading the biographies and arguments of famous mathematicians? Kurt Gödel’s incompleteness theorem, for example, made sense to me when I understood what David Hilbert was attempting at the time (to formalize math once and for all). Now I don’t just think of the incompleteness theorem as “some more math”, but as something that broke the hearts of mathematicians in its time.

Suddenly mathematicians aren’t aliens speaking a language I do not understand. They’re just, like, dudes. This isn’t meant in disrespect as I will almost certainly never be able to understand math to that level, but the point is these people wrote math with the expectation that it be read by other people.

It’s like software, I think, in that sense. Sure, most people cannot read code, but if they wanted to, they’d realize it takes some time, but not as long as they feared. Just as code has evolved into higher abstractions to aid human readability, math has evolved its syntax in various branches for easier manipulation. Mathematics is rife with different representations of the same thing (eg graphs and tables being ways to represent the same thing — with graphs giving more “at a glance” info). This is to make it easier for me — a fellow human! — to understand.

Lately I’ve been studying with MathAcademy. MathAcademy brags that their lessons are not “edutainment”, and that you should approach its platform with the assumptions that you will sweat. More a gym than a classroom. They say it’s like training for a marathon.

Cool. I’m a sucker for punishment.

Since then I’ve been reconstructing my mathematical foundations. Basic stuff: complex numbers, polynomials, trigonometry, some calculus and linear algebra). I’ve started making myself stare at equations and symbols and understand why this is currently the best way to represent it. All of a sudden, I’m seeing that there are generalizations you can make, such that when you see a new formula you’ve never encountered before, you can (faster now) understand and interpret what it does.

A side effect of this is I’ve picked up Haskell again, and with a better understanding of why Alonzo Church’s Lambda Calculus can be thought of as the human (ie, mathematical) computer to Alan Turing’s machine computer. This makes me appreciate the Haskell syntax, which used to feel rather hostile to me a few years ago.

I wouldn’t say I’m in love with math yet. I’m merely less terrified of it. I like this rhythm of testing mathematical concepts with a functional programming paradigm. In a moment of unbridled hubris, I even tried to use Lean.

Someday, maybe.

Thank you, friend, as always, for reading.